A writing streak is a consecutive series of writing, usually measured in days. Streaks are not unique to writing and are used to describe consecutive series of almost anything: winning, losing, physical activity, etc.
NaNoWriMo first implemented writing streaks on the NaNoWriMo website in 2015, with badges unlocked on the NaNoWriMo dashboard for updating your word count 5 days in a row, ten days in a row, and thirty days in a row (or every day in November).
The redesigned NaNoWriMo website in 2019 includes writing streaks for all projects on the dashboard, with separate badges unlocked for streaks of 2 days, 3 days, 7 days, 14 days, and 21 days. 2020 introduced a writing streak badge for the entire length of a Wrimo's goal (for example, 30 days for November's NaNoWriMo).
NaNoWriMo also introduced Web Badges to celebrate writing streaks in 2018 and 2019. The 2018 badges came about via email and social media during the first five days of November, while the 2019 badges featured 30 badges, from a 1-day streak to a 30-day streak.